The UTC Graduate School is pleased to announce that\u00a0Tanner Smith will present Doctoral research titled,\u00a0Optimization for a Sturm-Liouville Problem with the Spectral Parameter in the Boundary Condition on\u00a010\/06\/2022 at\u00a01:00-3:00pm in\u00a0Grote 317. Everyone is invited to attend.\u00a0
Computational Science
Chair:\u00a0Boris Belinskiy
Co-Chair:\u00a0
Abstract:
We find an optimal mass of a structure described by a Sturm-Liouville (S-L) problem with a spectral parameter in the boundary conditions. While previous work on the subject focused on a somewhat simplified model, we consider a more general S-L problem. We use the calculus of variations approach to determine a set of critical points of a corresponding mass functional, yet these critical points – which we call \\textit{predesigns} – do not themselves represent meaningful solutions. It is natural to expect a mass to be real and positive. To this end, we additionally introduce a set of solvability conditions on the S-L problem data, confirming that these critical points represent meaningful solutions we refer to as \\textit{designs}. We further present the analytic continuation of these predesigns in regards to the spectral parameter as well as a discussion of the stability of these (pre)designs. We present a code that allows us to for the given data of the S-L problem to check conditions of solvability, plot the design, and calculate the value of the functional that represents the optimal mass.<\/p>\n","protected":false},"excerpt":{"rendered":"
The UTC Graduate School is pleased to announce that\u00a0Tanner Smith will present Doctoral research titled,\u00a0Optimization for a Sturm-Liouville Problem with the Spectral Parameter in the Boundary Condition on\u00a010\/06\/2022 at\u00a01:00-3:00pm in\u00a0Grote 317. Everyone is invited to attend.\u00a0 Computational Science Chair:\u00a0Boris Belinskiy Co-Chair:\u00a0 Abstract: We find an optimal mass of a structure described by a Sturm-Liouville (S-L)… <\/p>\n